1. Field of the Invention
The present invention is directed to an undulator, and, more particularly, to the undulator which provides an increased range of variable wavelength of a radiation light.
2. Description of the Related Art
An undulator is a device which produces a radiation light by allowing an electron beam into a resonant cavity in which a standing electromagnetic wave is existent. The electron beam interacts with both the electric field and the magnetic field of the standing electromagnetic wave, and emits a radiation light in the course of travel along its sinuous curve path. The undulator is typically included in a linear portion of an electron storage ring and the like. Although the radiation light obtained by the undulator has characteristics similar to those of the laser light, the wavelength of the radiation light ranges from visible light further into the X-ray region, and light intensity of the radiation light in the X-ray region is stronger than those of other light sources by one to three orders of magnitude. As a high-powered X-ray, the radiation light finds many applications in a variety of fields, such as in the study of molecular structures and the pattern transfer in the manufacturing of VLSIs and ULSIs.
FIG. 7 is a perspective view showing schematically the construction of a conventional undulator. The undulator comprises a waveguide 10 forming a resonant cavity and a power feeding waveguide 12 generating standing electromagnetic wave inside the cavity. With the electromagnetic wave 20 fed through the input of the power feeding waveguide 12, a standing electromagnetic wave is generated, as shown in FIG. 8, inside the waveguide 10 which forms a sealed resonant cavity. When an electron beam 4 is introduced, via a hole 10a, into the waveguide 10 with the standing electromagnetic wave in it, a radiation light 5 is produced and emitted outwardly via a hole 10b.
FIG. 8 is a perspective view showing schematically the relationship of the spatial distribution of electromagnetic wave, incident electron beam, and output the radiation light, in the conventional undulator which is disclosed in an article entitled "Development of Microwave Undulator" by Tumori Shintake et al. (Japanese Journal of Applied Physics, Vol. 22, No. 5, pp. 844-851, May 1983).
In FIG. 8, the electron beam 4 is directed into a resonant cavity (not shown) at a speed of v. The electron beam 4 travels in a sinuous curve path while interacting with both an electric field 6 and a magnetic field 7 of the standing electromagnetic wave inside the resonant cavity, and emits a radiation light 5. The following Lorentz force F exerts on the electron beam 4 while it is being interacting with both the electric field 6 and the magnetic field 7 during its motion. EQU F=eE+ev.times.B (1)
where e is a charge of an electron, and vectors E, B and V are the electric and magnetic field strengths, and the speed of electron, respectively. In the undulator, the following electric and magnetic fields take place. EQU Ex=E.sub.O sin(2.pi.z/.lambda.g)sin(.omega.t) (2) EQU By=B.sub.O cos(2.pi.z/.lambda.g)cos(.omega.t) (3)
where x, y and z are three mutually perpendicular directions, with x being the vertical direction, y the horizontal direction and z the direction of propagation of the electron beam; t is time, .lambda. g is the guide wavelength of the electromagnetic wave in the cavity, E.sub.O and B.sub.O are the peak electric and magnetic field strengths, and .omega. is the angular frequency of the electromagnetic wave. From the above equations, the Lorentz force is expressed as follows: EQU Fz=e{E.sub.O sin(2.pi.z/.lambda.g)sin(.omega.t) -evB.sub.O cos(2.pi.z/.lambda.g)cos(.omega.t)} (4)
The position z of an electron traveling at a speed of v is vt. The angular frequency .omega. is 2.pi.c/.lambda..sub.O (.lambda..sub.O is the wavelength of the electromagnetic wave in free space, and c is the speed of light). Thus, EQU Fz=-e/2[(B.sub.O +E.sub.O)cos2.pi.{1/.lambda.g+c/(v.lambda..sub.O)}z+(vB.sub.O -E.sub.O)cos2.pi.{1/.lambda.g-c/(v.lambda..sub.O)}z] (5)
Generally, the speed v of electron is nearly equal to the speed of light. Assuming that the permittivity .epsilon. and the permeability .mu. in the cavity are equal to those values in the vacuum, (vB.sub.O -E.sub.O) becomes nearly equal to zero. The equation (5) is thus approximated as follows: EQU Fz=-e/2(vB.sub.O +E.sub.O)cos2.pi.{1/.lambda.g+c/(v.lambda..sub.O)}z (6)
The period A u of the undulator is EQU .lambda.u=.lambda..sub.O .lambda.g/(.lambda..sub.O +c.lambda.g/v)(7)
where the guide wavelength .lambda.g of the electromagnetic wave (FIG. 8) is determined by the following equation. EQU 1/.lambda.g=(1/.lambda..sub.O.sup.2 -1/.lambda.c.sup.2).sup.1/2( 8)
where .lambda.c is the cutoff wavelength determined by the configuration of the cavity, and .lambda..sub.O (the wavelength of the electromagnetic wave in free space) is set to a value which satisfies the resonant conditions under which c/.lambda..sub.O is equal to the resonance frequency of the cavity. From equations (7) and (8), the undulator period .lambda.u is a fixed value in the conventional undulator.
The guide wavelength of the electromagnetic wave in the waveguide is .lambda.g. Viewed from the travelling electron beam 4, however, the wavelength of the electromagnetic wave agrees with the undulator period .lambda.u, in which electric and magnetic field strengths of the electromagnetic wave vary sinusoidally with time.
In the conventional undulator, its cavity in which the standing electromagnetic wave is generated is of a semi-sealed construction with a predetermined configuration. Thus, the configuration of the cavity remains fixed rather than adjustable. To meet the resonance condition, the guide wavelength .lambda.g must be a fixed value as described above. Thus, the wavelength of the electromagnetic wave (the undulator period .lambda.u) is also a fixed value.
The waveform .lambda. of radiation light is EQU .lambda.=.lambda.u(1+K.sup.2 /z)/2.lambda..sup.2 ( 9) EQU K .varies. B.sub.O .multidot..lambda.u (10)
where .lambda. is the electron energy divided by the electron rest energy, and B.sub.O is the peak magnetic strength in the undulator.
To vary the wavelength of the radiation light, either the undulator period .lambda.u or the peak magnetic field intensity B.sub.O must be varied. In the conventional undulator, however, the undulator period .lambda.u remains constant. Although the wavelength .lambda. of the electromagnetic wave may be slightly varied by varying the peak magnetic field intensity B.sub.O by controlling the input power of the electromagnetic wave 20 fed through the power feeding waveguide 12 in FIG. 7, no substantial change of the wavelength .lambda. of the radiation light is possible.
Equations (9) and (10) obviously shows that varying the undulator period .lambda. results in a greater change in the wavelength .lambda. of the radiation light than varying the peak magnetic field intensity B.sub.O.